Density Functional Theory Study of Triple Transition Metal Cluster Anchored on the C2N Monolayer for Nitrogen Reduction Reactions

The electrochemical nitrogen reduction reaction (NRR) is an attractive pathway for producing ammonia under ambient conditions. The development of efficient catalysts for nitrogen fixation in electrochemical NRRs has become increasingly important, but it remains challenging due to the need to address the issues of activity and selectivity. Herein, using density functional theory (DFT), we explore ten kinds of triple transition metal atoms (M3 = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) anchored on the C2N monolayer (M3-C2N) as NRR electrocatalysts. The negative binding energies of M3 clusters on C2N mean that the triple transition metal clusters can be stably anchored on the N6 cavity of the C2N structure. As the first step of the NRR, the adsorption configurations of N2 show that the N2 on M3-C2N catalysts can be stably adsorbed in a side-on mode, except for Zn3-C2N. Moreover, the extended N-N bond length and electronic structure indicate that the N2 molecule has been fully activated on the M3-C2N surface. The results of limiting potential screen out the four M3-C2N catalysts (Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N) that have a superior electrochemical NRR performance, and the corresponding values are −0.61 V, −0.67 V, −0.63 V, and −0.66 V, respectively, which are smaller than those on Ru(0001). In addition, the detailed NRR mechanism studied shows that the alternating and enzymatic mechanisms of association pathways on Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N are more energetically favorable. In the end, the catalytic selectivity for NRR on M3-C2N is investigated through the performance of a hydrogen evolution reaction (HER) on them. We find that Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N catalysts possess a high catalytic activity for NRR and exhibit a strong capability of suppressing the competitive HER. Our findings provide a new strategy for designing NRR catalysts with high catalytic activity and selectivity.


Introduction
Ammonia (NH 3 ) is an important raw chemical material that plays an essential role in industry, agricultural production, energy storage and conversion, and other fields [1][2][3].At present, industrial ammonia synthesis mainly relies on the traditional Haber-Bosch process [4,5].Since this technology requires high temperatures and pressure, it not only consumes vast energy, but also emits a large amount of greenhouse gasses.Therefore, against the backdrop of the energy crisis and increasing environmental concerns, developing new processes for efficiently synthesizing ammonia under mild conditions is urgent [6].
Compared with the Haber-Bosch method, the electrocatalytic approach for achieving nitrogen reduction reactions (NRRs) can theoretically be carried out at room temperature and pressure [7,8].Meanwhile, the sources of raw water and nitrogen are extensive, which provides an opportunity for achieving the green synthesis of ammonia under mild conditions [9].In recent years, electrocatalytic nitrogen reduction for ammonia production has attracted significant attention, and related research has shown a rapid growth trend [10][11][12][13].However, the current study shows that although electrocatalytic technology can achieve the green synthesis of ammonia, the thermodynamic and kinetic obstacles to the production of ammonia via electrocatalytic nitrogen reduction at room temperature and pressure are enormous due to the high stability of the N≡N triple bond and the slow adsorption of nitrogen [14,15].Moreover, the selectivity of the nitrogen reduction reaction and the ammonia production rate are greatly reduced due to the hydrogen precipitation competition reaction [16].Therefore, how to improve the ammonia production rate and the catalyst selectivity at the same time is the biggest challenge in the study of electrocatalytic nitrogen reduction at ambient temperature and pressure.
The two-dimensional material known as C 2 N has recently emerged as a subject of interest among researchers, thanks to its remarkable stability, cavity structure, high specific surface area, and other distinctive attributes [17][18][19][20].Its spacious cavities make C 2 N a suitable support for anchoring metal atoms to catalyze various chemical reactions [21].Metal clusters featuring exposed atomic interfaces and distinct electronic configurations have garnered significant attention in multiphase catalysis [22].Transition metals like Fe-, Ru-, and Co-based complexes, with their d-orbitals capable of donating electrons to the empty π*-orbitals of N 2 and accepting electrons from its σ-orbitals, enhance N 2 adsorption, making them suitable for nitrogen reduction reaction (NRR) catalysis [23][24][25][26].In response to the rising interest in single-atom catalysts for efficient NRR electrocatalysts [27][28][29], dualatom and triple-atom catalysts have also been experimentally and theoretically explored for their catalytic performance in NRRs [30][31][32].For instance, the work proposed by Chen et al. indicates that due to the unique characteristics of M 3 (M = Mn, Fe, Co, and Ni) active sites, the triple-atom catalysts exhibit better catalytic activity towards NRRs than single-atom and double-atom catalysts [33].Liu et al. studied Fe 3 clusters anchored on the surface of Al 2 O 3 as multiphase catalysts for NRRs [34].They discovered that their comparable activity to Ru catalysts, which is attributed to the large spin polarization, low iron oxidation state, and multi-step oxidation-reduction ability of Fe 3 clusters.
Motivated by the above studies, a series of triple transition metal atoms (M 3 = 3d transition metal, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) anchored on the C 2 N monolayer (M 3 -C 2 N) are designed as electrocatalysts for NRRs, and the electronic structures and NRR catalytic mechanisms are systematically investigated using density functional theory (DFT).Firstly, the binding energy of triple transition metal atoms on C 2 N is calculated to evaluate the stability of M 3 -C 2 N catalysts to prescreen the promising candidates for NRR catalysts.The negative binding energies manifest that the triple transition metal clusters can be stably anchored on the N6 cavity of the C 2 N monolayer.Next, as the first step of the NRR, the adsorption and activation of N 2 molecules on the surface of M 3 -C 2 N are studied via the adsorption structure, adsorption energy, and electronic structures.Moreover, the catalytic activity and mechanisms are systematically investigated based on the Gibbs free energy of the whole NRR process.According to the limiting potential, we screen out four highly active NRR catalysts, including Co 3 -C 2 N, Cr 3 -C 2 N, Fe 3 -C 2 N, and Ni 3 -C 2 N, while they can suppress the competitive hydrogen evolution reaction.Among them, Co 3 -C 2 N exhibits the highest NRR activity with a limiting potential of −0.61 V.This study provides a comprehensive understanding of the stability, activity, and selectivity of M 3 -C 2 N as NRR catalysts, which can guide the further experimental exploration of M 3 -C 2 N or other related reactions.

Structure and Stability of M 3 -C 2 N
The pristine C 2 N monolayer containing 48 C and 24 N atoms is optimized, and the optimized lattice constant is a × b = 16.83Å × 16.77 Å, which is consistent with the previous literature [35,36].As shown in Figure 1a, the N6 cavity of the C 2 N structure is 5.56 Å, which is large enough to anchor triple metal atoms.Moreover, the N atoms surrounding the N6 cavity exhibit electron-rich properties, and due to the electron loss of the C atom, the N atom is negatively charged.Therefore, N atoms endow the N6 cavity environment with high electron enrichment properties, making the cavity an ideal place to contain positively charged TM ions. Figure 1b exhibits the optimized structure of Co triple metal clusters anchored on the N6 cavity of C 2 N, and other optimized structures of M 3 -C 2 N are displayed in the Supplementary Materials (Figure S1).The average bond length of the Co-N bond is 1.89 Å, indicating a strong interaction between Cu and N atoms.In addition, the difference in charge density clearly shows the accumulation and depletion of charges around the Co and adjacent N atoms.It is worth noting that the high charge density around the Co atoms facilitates the subsequent adsorption of N 2 molecules.To evaluate the stability of the M 3 -C 2 N catalysts, the binding energy of triple transition metal atoms on the C 2 N monolayer is calculated, as displayed in Figure 1c.The ∆E b values of all catalysts are less than 0 eV, confirming the stability of the M 3 -C 2 N system and the triple transition metal clusters stably anchored on the N6 cavity of the C 2 N monolayer.

Structure and Stability of M3-C2N
The pristine C2N monolayer containing 48 C and 24 N atoms is optimized, and the optimized lattice constant is a × b = 16.83Å × 16.77 Å, which is consistent with the previous literature [35,36].As shown in Figure 1a, the N6 cavity of the C2N structure is 5.56 Å, which is large enough to anchor triple metal atoms.Moreover, the N atoms surrounding the N6 cavity exhibit electron-rich properties, and due to the electron loss of the C atom, the N atom is negatively charged.Therefore, N atoms endow the N6 cavity environment with high electron enrichment properties, making the cavity an ideal place to contain positively charged TM ions. Figure 1b

N2 Adsorption on M3-C2N
For the whole NRR process, the adsorption and activation of N2 molecules on the catalyst surface is a crucial step.Therefore, the adsorption performance of N2 on the surface of M3-C2N catalysts is investigated, and the adsorption configurations are shown in Figure 2. It can be seen that except for on Zn3-C2N, N2 is more energetically favorable when adsorbed in the side-on mode on all M3-C2N, which is consistent with the research findings in the literature.Compared with the N-N bond length (1.12 Å) of free N2 molecule,

N 2 Adsorption on M 3 -C 2 N
For the whole NRR process, the adsorption and activation of N 2 molecules on the catalyst surface is a crucial step.Therefore, the adsorption performance of N 2 on the surface of M 3 -C 2 N catalysts is investigated, and the adsorption configurations are shown in Figure 2. It can be seen that except for on Zn 3 -C 2 N, N 2 is more energetically favorable when adsorbed in the side-on mode on all M 3 -C 2 N, which is consistent with the research findings in the literature.Compared with the N-N bond length (1.12 Å) of free N 2 molecule, the N-N bond length of N 2 after adsorption has been elongated to varying degrees, indicating that N 2 has been activated on M 3 -C 2 N. On Zn 3 -C 2 N, the bond length of N-N is still 1.12 Å, and N 2 is far from the catalyst surface, indicating that the N 2 molecule cannot be adsorbed on it, so the NRR activity of Zn 3 -C 2 N will not be discussed later.In addition, the charge density differences plot also suggests that the adsorbed N 2 interacts with M 3 -C 2 N, activating the N≡N triple bond.The adsorption energies of N 2 on the surface of M 3 -C 2 N catalysts are summarized in Figure 3a.It can be seen that the adsorption of N 2 on Sc 3 -C 2 N, Ti 3 -C 2 N, and V 3 -C 2 N is exceedingly strong, and the E ads-N2 values are −3.78eV, −3.96 eV, and −3.23 eV, respectively.The adsorption strength of N 2 on Cu 3 -C 2 N is the most weak with only −0.17 eV values of E ads-N2 .The range of adsorption energy values on the other six catalysts is from −0.84 eV to −1.60 eV.To further elucidate the adsorption and activation of N 2 , the scaling relationship between the charge transfer from M 3 -C 2 N to the adsorbed N 2 and the adsorption energy E ads-N2 is studied and displayed in Figure 3b.It can be seen that the most charge transfer is from M 3 -C 2 N to N 2 on Sc 3 -C 2 N, Ti 3 -C 2 N, and V 3 -C 2 N, corresponding to 1.84e, 1.62e, and 1.33e, respectively, which is consistent with the adsorption strength of them and the N-N bond length of adsorbed N 2 .There is a significant positive correlation between charge transfer and E ads-N2 .That is to say, the more charge transfer, the stronger the N 2 adsorption, and the more negative the value of E ads-N2 .In order to better understand the adsorption of N 2 , the project density of states of the M 3 -C 2 N after adsorption of N 2 is shown in Figure 3c,d

NRR Mechanism and Activity on M3-C2N
The dissociation and association pathways are the two common mechanisms for electrocatalytic NRRs.For the dissociation pathway, it is difficult for the catalyst to break the N≡N bond of the adsorbed N2 molecule.Therefore, only the association pathway on M3-C2N is investigated in this work.For the association pathway, before the formation of the first NH3 molecule, the two N atoms of N2 remain bound to each other.It can be further divided into the distal and consecutive mechanisms (the protons continuously attack a N atom until the first NH3 molecule is produced), as well as the alternating and enzymatic mechanisms (the protons alternately bind the two N atoms).Herein, the two NRR mechanisms on Co3-C2N are shown in Figure 4a, and the adsorbed N2 molecule is gradually hydrogenated to produce NH3 gas.As we all know, the activity of electrocatalysts can be estimated by the limit potential (UL).Therefore, the UL values of the M3-C2N catalysts are calculated and displayed in Figure 4b, and the Ru(0001) (UL = 0.98 eV) catalyst is chosen as a benchmark to evaluate the electrocatalytic NRR activity of M3-C2N due to it having the highest theoretical activity on the surface of the bulk metal.It can be seen that the UL values of Sc3-C2N, Ti3-C2N, and V3-C2N are larger than that of Ru(0001), indicating their poor catalytic activity for NRR.The other six M3-C2N catalysts with UL values less than 0.98 eV exhibit a better catalytic activity than Ru(0001).It is worth noting that the limit potential of Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N are relatively small, and the corresponding values are −0.61V, −0.67 V, −0.63 V, and −0.66 V, so their free energy diagrams for NRRs are detailed in Figure 5.It can be seen that for Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N, the step of *NNH → *NHNH is more significant downhill than the *NNH →

Selectivity Evaluation for NRR on M 3 -C 2 N
Furthermore, an ideal electrocatalyst for NRR should possess a high stability and activity and effectively suppress the hydrogen evolution reaction (HER) to achieve high production for NH 3 .The HER is the most problematic yet dominant side reaction in the NRR.Therefore, the adsorption free energy of H (∆G *H ) on M 3 -C 2 N catalysts is calculated and summarized in Figure 6a.If the ∆G *H values are close to 0 eV, it means that H* cannot easily cover the metal surface and will not block the active sites for NRRs.Although, the ∆G *H values on all M 3 -C 2 N are lower than those on Ru(0001) (∆G *H = −0.35eV), some M 3 -C 2 N exhibit a relatively high HER activity, indicating that the HER process that occurred on some M 3 -C 2 N surfaces could be hindered effectively.In addition, the difference in limiting potential between the NRR and HER (U L (NRR)-U L (HER)) is calculated to estimate the catalytic selectivity for NRR on M

Selectivity Evaluation for NRR on M3-C2N
Furthermore, an ideal electrocatalyst for NRR should possess a high stability and activity and effectively suppress the hydrogen evolution reaction (HER) to achieve high production for NH3.The HER is the most problematic yet dominant side reaction in the NRR.Therefore, the adsorption free energy of H (ΔG*H) on M3-C2N catalysts is calculated and summarized in Figure 6a.If the ΔG*H values are close to 0 eV, it means that H* cannot easily cover the metal surface and will not block the active sites for NRRs.Although, the ΔG*H values on all M3-C2N are lower than those on Ru(0001)(ΔG*H = −0.35eV), some M3-C2N exhibit a relatively high HER activity, indicating that the HER process that occurred on some M3-C2N surfaces could be hindered effectively.In addition, the difference in limiting potential between the NRR and HER (UL(NRR)-UL(HER)) is calculated to estimate the catalytic selectivity for NRR on M3-C2N; the scaling relationship between the UL(NRR)-UL(HER) and UL(NRR) is plotted in Figure 6b.Notably, Mn3-C2N, Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N have a relatively high NRR selectivity.Therefore, Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N not only possess a high NRR activity, but also exhibit the highest selectivity for NRRs.

Computational Methods
All computational studies were executed utilizing the Perdew−Burke−Ernzerhof (PBE) functional [37] implemented in the Vienna Ab Initio Simulation Package (VASP

Computational Methods
All computational studies were executed utilizing the Perdew−Burke−Ernzerhof (PBE) functional [37] implemented in the Vienna Ab Initio Simulation Package (VASP 5.4.4) [38,39].Spin polarization was incorporated in all calculations, and the electron-ion interactions were described through the projector-augmented wave method with a 450 eV cutoff energy.Atomic structures were fully relaxed until the force on each atom was smaller than 0.02 eV/Å, while the energy convergence was set to 10 −5 eV.To account for van der Waals (vdW) interactions, Grimme's DFT-D3 approach was implemented [40].For geometry relaxation, a 3 × 3 × 1 k-point grid centered at the gamma point was employed, and a 20 Å vacuum space along the z-direction was introduced to prevent periodic image interactions.To simulate the electrolyte solution and address solvation effects, the VASPsol code with an implicit solvation model was utilized [41,42].
The binding energy of triple transition metal atoms on a C 2 N monolayer is calculated to evaluate the stability of M 3 on the C 2 N monolayer: where E M3-C2N , E C2N , and E M are the total energies of M 3 -C 2 N, C 2 N, and metal atoms, respectively.The adsorption energies of reaction species on the M 3 -C 2 N catalyst are determined by: where E tot and E species are the total energies of the M 3 -C 2 N with adsorbed reaction species and the isolated reaction species.
Based on the computational hydrogen electrode (CHE) model given by Nørskov and coworkers, the Gibbs free energy change (∆G) for each fundamental step of the NRR is obtained by using the following equation: where ∆E is the reaction energy difference in each hydrogenation step in the NRR pathways.∆ZPE and T∆S are the changes in zero-point energy and entropy (T = 298.15K), respectively.Limiting potential (U L ) was obtained from the maximum free energy change (∆G max ) among all elementary steps along the lowest-energy pathway by: U L = −∆G max /e (4)

Conclusions
In summary, the triple transition metal atoms (M 3 = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) anchored on the C 2 N monolayer (M 3 -C 2 N) as electrocatalysts for NRRs are systematically investigated.Based on the negative binding energies of triple transition metal clusters on C 2 N, the conclusion can be drawn that these ten metal clusters can be stably anchored on the N6 cavity of the C 2 N structure.The N 2 adsorption results indicate that except for Zn 3 -C 2 N, the N 2 molecule can be stably adsorbed in the side-on mode on all the M 3 -C 2 N catalysts.In addition, the results combining adsorption configurations and electronic structure demonstrate that the charges transfer from the M 3 -C 2 N to N 2 , activating the N 2 molecule.The positive correlation of the scaling relationship between the charge transfer and the adsorption energy illustrates that the more charge transfer, the stronger the N 2 adsorption.The analysis of Gibbs free energy changes suggests that the alternating and enzymatic mechanisms of the association pathway on Co 3 -C 2 N, Cr 3 -C 2 N, Fe 3 -C 2 N, and Ni 3 -C 2 N, which have the relatively low limiting potentials of −0.61 V, −0.67 V, −0.63 V, and −0.66 V, are more energetically advantageous.Moreover, the potential-limiting step (PDS) on both Co 3 -C 2 N and Ni 3 -C 2 N is the *NHNH 2 → *NH 2 NH 2 step, while that on Cr 3 -C 2 N and Fe 3 -C 2 N is the step of *NH 2 → *NH 3 .Finally, we investigate the competitive reaction of HER on M 3 -C 2 N, and it can be concluded that five catalysts (including Mn 3 -C 2 N, exhibits the optimized structure of Co triple metal clusters anchored on the N6 cavity of C2N, and other optimized structures of M3-C2N are displayed in the supporting information.The average bond length of the Co-N bond is 1.89 Å, indicating a strong interaction between Cu and N atoms.In addition, the difference in charge density clearly shows the accumulation and depletion of charges around the Co and adjacent N atoms.It is worth noting that the high charge density around the Co atoms facilitates the subsequent adsorption of N2 molecules.To evaluate the stability of the M3-C2N catalysts, the binding energy of triple transition metal atoms on the C2N monolayer is calculated, as displayed in Figure1c.The ∆Eb values of all catalysts are less than 0 eV, confirming the stability of the M3-C2N system and the triple transition metal clusters stably anchored on the N6 cavity of the C2N monolayer.

Figure 1 .
Figure 1.(a) Optimized structure of C2N.(b) The charge density difference of Co3-C2N.(Isosurface = 0.003 e/Bohr 3 .Yellow represents the charge increase, and cyan represents the charge decrease.)(c) The binding energy of triple transition metal atoms on the C2N monolayer.

Figure 1 .
Figure 1.(a) Optimized structure of C 2 N. (b) The charge density difference of Co 3 -C 2 N. (Isosurface = 0.003 e/Bohr 3 .Yellow represents the charge increase, and cyan represents the charge decrease.)(c) The binding energy of triple transition metal atoms on the C 2 N monolayer.
, taking the strongest adsorption on Ti 3 -C 2 N and the weakest adsorption on Zn 3 -C 2 N as examples.It can be seen that for Ti 3 -C 2 N, there is a significant orbital hybridization between the Ti-d and N-p orbitals.For Zn 3 -C 2 N, due to weak adsorption, the N 2 molecule still maintains a high DOS without orbital hybridization with Zn-d.

Figure 2 .
Figure 2. Optimized adsorption configurations and charge density differences of N 2 adsorbed on M 3 -C 2 N. The isosurface value is 0.003 e/Bohr 3 .

Figure 3 .
Figure 3. (a) Adsorption energies of N 2 on the M 3 -C 2 N catalysts.(b) Charge transfer from M 3 -C 2 N to the adsorbed N 2 as a function of E ads-N2 .The partial density of states (PDOS) of N 2 on (c) Ti 3 -C 2 N and (d) Zn 3 -C 2 N.

2. 3 .
NRR Mechanism and Activity on M 3 -C 2 N The dissociation and association pathways are the two common mechanisms for electrocatalytic NRRs.For the dissociation pathway, it is difficult for the catalyst to break the N≡N bond of the adsorbed N 2 molecule.Therefore, only the association pathway on M 3 -C 2 N is investigated in this work.For the association pathway, before the formation of the first NH 3 molecule, the two N atoms of N 2 remain bound to each other.It can be further divided into the distal and consecutive mechanisms (the protons continuously attack a N atom until the first NH 3 molecule is produced), as well as the alternating and enzymatic mechanisms (the protons alternately bind the two N atoms).Herein, the two NRR mechanisms on Co 3 -C 2 N are shown in Figure 4a, and the adsorbed N 2 molecule is gradually hydrogenated to produce NH 3 gas.As we all know, the activity of electrocatalysts can be estimated by the limit potential (U L ).Therefore, the U L values of the M 3 -C 2 N catalysts are calculated and displayed in Figure 4b, and the Ru(0001) (U L = 0.98 eV) catalyst is chosen as a benchmark to evaluate the electrocatalytic NRR activity of M 3 -C 2 N due to it having the highest theoretical activity on the surface of the bulk metal.It can be seen that the U L values of Sc 3 -C 2 N, Ti 3 -C 2 N, and V 3 -C 2 N are larger than that of Ru(0001), indicating their poor catalytic activity for NRR.The other six M 3 -C 2 N catalysts with U L values less than 0.98 eV exhibit a better catalytic activity than Ru(0001).It is worth noting that the limit potential of Co 3 -C 2 N, Cr 3 -C 2 N, Fe 3 -C 2 N, and Ni 3 -C 2 N are relatively small, and the corresponding values are −0.61V, −0.67 V, −0.63 V, and −0.66 V, so their free energy diagrams for NRRs are detailed in Figure 5.It can be seen that for Co 3 -C 2 N, Cr 3 -C 2 N, Fe 3 -C 2 N, and Ni 3 -C 2 N, the step of *NNH → *NHNH is more significant downhill than the *NNH → *NNH 2 step, indicating that the alternating and enzymatic mechanisms on them are more energetically advantageous.In addition, the first step of the NRR shows goes downhill for all four M 3 -C 2 N catalysts, precisely because of the strong N 2 adsorption, which also suggests that the adsorption and activation of N 2 molecules can occur at room temperature.The potential-limiting step (PDS) on Co 3 -C 2 N and Ni 3 -C 2 N is the *NHNH 2 → *NH 2 NH 2 step, and the corresponding ∆G values are 0.61 eV and 0.66 eV.For Cr 3 -C 2 N and Fe 3 -C 2 N, the final step of hydrogenation *NH 2 → *NH 3 is the PDS; and their ∆G values are 0.67 eV and 0.63 eV.Therefore, Co 3 -C 2 N, Cr 3 -C 2 N, Fe 3 -C 2 N, and Ni 3 -C 2 N are the candidates for NRR catalysts, and Co 3 -C 2 N possesses the highest NRR activity.*NNH2 step, indicating that the alternating and enzymatic mechanisms on them are more energetically advantageous.In addition, the first step of the NRR shows goes downhill for all four M3-C2N catalysts, precisely because of the strong N2 adsorption, which also suggests that the adsorption and activation of N2 molecules can occur at room temperature.The potential-limiting step (PDS) on Co3-C2N and Ni3-C2N is the *NHNH2 → *NH2NH2 step, and the corresponding ΔG values are 0.61 eV and 0.66 eV.For Cr3-C2N and Fe3-C2N, the final step of hydrogenation *NH2 → *NH3 is the PDS; and their ΔG values are 0.67 eV and 0.63 eV.Therefore, Co3-C2N, Cr3-C2N, Fe3-C2N, and Ni3-C2N are the candidates for NRR catalysts, and Co3-C2N possesses the highest NRR activity.

Figure 4 .
Figure 4. (a) Schematic diagram of the NRR catalyzed by Co 3 -C 2 N and the corresponding adsorption intermediate.(b) Theoretical limiting potential U L of M 3 -C 2 N.
3 -C 2 N; the scaling relationship between the U L (NRR)-U L (HER) and U L (NRR) is plotted in Figure 6b.Notably, Mn 3 -C 2 N, Co 3 -C 2 N, Cr 3 -C 2 N, Fe 3 -C 2 N, and Ni 3 -C 2 N have a relatively high NRR selectivity.Therefore, Co 3 -C 2 N, Cr 3 -C 2 N, Fe 3 -C 2 N, and Ni 3 -C 2 N not only possess a high NRR activity, but also exhibit the highest selectivity for NRRs.

Figure 6 .
Figure 6.(a) Free energy diagrams for the HER on M 3 -C 2 N. (b) Liming potential (U L ) versus U L (NRR)-U L (HER) on M 3 -C 2 N.